Device and method for measuring gravitation

ABSTRACT

Gravitation in three dimensions is measured using an accelerometer attached to a carrier, a satellite navigation receiver and a computer. The satellite navigation receiver determines a position and attitude, and changes in the position and attitude over time. The computer calculates complete kinematics in inertial space from the timely changes of the determined position and attitude and calculates the gravitation by subtracting the kinematic acceleration from the one observed by the accelerometer. In a preferred embodiment the accelerometer is connected tightly to the carrier. At most, damping elements may be mounted between the accelerometer and the carrier. The accelerometer can be a single accelerometer or a triplet of non-parallel accelerometers. The satellite navigation receiver may be one instrument equipped with three or more antennae or a set of three or more single instruments connected to each other. A time signal of the satellite navigation receiver is used for synchronizing the acceleration measurements. More specifically, the time signal of the satellite navigation receiver may be utilized for controlling the gate time of a counter, which counts an acceleration proportional frequency generated for signal evaluation.

The present invention relates to a device and a method for observinggravitation in accordance with the preambles of the independent claims.

The so called gravimetry or measurement of gravitation has to beclassified as a special field of measurement technology, essential forthe determination of the gravity field of the earth, thereby forregional and global geodesy, geology or geophysics includingexploration, satellite orbit determination, precise navigationespecially by inertial navigation instruments etc.

Devices for observing gravity earlier were based on the principle ofpendulum observations, today either on the principle of precise trackingof a throw-/fall trajectory (few dm length inside a vacuum chamber) oron the principle of a spring balance (constant mass, determination offorce). They also may be assigned to the more general class ofaccelerometers, as vice versa gravimeters may be seen as accelerometersparticularly suited for gravity observations. Gravimeters also stand outfrom accelerometers in general by their significantly increased naturalperiod. The predominant number of accelerometers or gravimeters,respectively, is based on the principle of a spring balance withconstant mass, where frequently (and also for the accelerometers used inthis case) the proof mass is kept in a null position also under varyingaccelerations by a feedback system of a (e.g., capacitive) pickoff and a(e.g., inductive) restoring force; the necessary current is a measure ofthe acceleration.

The pertinent state of the art is published particularly in TORGE, W.:Gravimetry, DeGruyter, Berlin, New York 1989, and in a conferenceproceedings volume, COLOMBO, O.(ed.): From Mars to Greenland: ChartingGravity with Space and Airborne Instruments, Symposium no 110, SpringerVerlag, New York etc. 1991.

In explanation of a few terms used:

Accurancy/resolution: The term accuracy will be limited to thedescription of instrumental performance in the sense of a mean error ina usual modeling. For the description of the quality of a solution foundfor the gravitational field of the earth sought after the term accuracyis dangerous: A quantitative description of the gravitational field ofthe earth always is the result of many individual observations and asubsequent evaluation, leading somehow to a surface function. Thecharacterizing of the said surface function by an accuracy value wouldneglect, to what area the said value refers. Because for the mean valueof a larger area more values are available in general, a better accuracyvalue--i.e., a smaller mean error--would be in place for a given task;this--however--contradicts the plausible notion. For this case, the termof resolution is more suitable. Although also not sharply defined, onemay imagine the following: The surface function may be approximated bymeans of e.g., a two dimensional trigonometric series, i.e., by a seriesof waves of graded wavelengths, in both directions. The wave with theshortest wavelength with a significantly nonzero amplitude correspondsto the resolution. This interpretation also is not totally strict,because e.g., the level of significance and the grading of thewavelength anticipated might be questioned. For our purpose, however,such a discussion is not necessary.

Gravitation: In connection with gravimetry at the earth one usuallytalks of the gravity field. In the following the term gravitation willbe preferred, because--as a matter of fact--predominantly gravitation isdealt with. `Gravitation` denotes the specific force with the unit m/s²corresponding to the unit of an acceleration. It is reminded, however,that the so called gravity is composed of the gravitation and thecentrifugal acceleration because of the rotation of the earth. Thelatter amounts to a maximum of 5% of gravitation.

Inertial space: Any change of motion of a mass requires a force andenergy, respectively, because of the inertia, even if the neargravitational masses would be removed. A space (thought as empty in thenear vicinity) with a reference frame with respect to which motionchanges can be observed, is an inertial space.

Attitude: For the geometric coordination of an non-punctual body to areference frame it is necessary to know not only its position, but alsoits direction. It may be named orientation. It is characterized by theangles with respect to the axes of the said reference frame.

One basic difficulty with gravimetry from moving carriers is the factthat on grounds of the principle of equivalence, an accelerometerindicates the sum of gravitational acceleration g and kinematicacceleration b , a=b+g. If one is interested in the gravitationalacceleration g only, one has to eliminate the kinematic acceleration b(from the motion of the carrier) somehow. In the classical procedure,one uses two complementary methods:

1. The gravimeter is isolated from the rotations of the carrier with theaid of a gyro-stabilized platform, thus the input axis of the sensor iskept vertical.

2. One tries to keep the translational motions small, especially thevertical motions, e.g., by using big aircraft and ships and/or specialefforts for stabilizing and steering. The remaining kinematic verticalaccelerations b are filtered out by long averaging period for theobservations a , such that g remains. To some extent, b is determinedalso by observations of positions or barometers; this, however, only forthe vertical component and without regard of the attitude of theaircraft and its changes.

Because gravitation basically is a vector quantity, a determination ofits three components is interesting. Vector gravimetry is not realizedyet, one limits oneself to the vertical component.

Conventional airborne or ship borne gravimetry bear a number ofdrawbacks. It is quite expensive because of gyro-stabilized platforms,bigger vehicles and high steering expenditure.

The gravimeters used are suited only for the determination of thevertical component, vector gravimetry is not possible thereby. Wherehorizontal components of the acceleration of the carrier are measuredanyway, so only because of the correction of the vertical component forthe cross-coupling effect. The long natural period of the gravimetersused does not allow an integration in phase with other quantities at asampling rate of 1 Hertz or more.

The kinematic accelerations b are either not recorded and thuseliminated as stochastic in a low pass filter, hence the filtered signala is equated with the gravitation g; as far as the kinematicaccelerations are recorded, e.g., by determination of the changes ofvertical position by means of satellite navigation or barometer, thenonly in the vertical component; these are also lowpass filtered ingeneral.

The potential of positioning by means of satellite navigation(particularly of the GPS system, "Global Positioning System") forgravimetry until now is utilized only for positioning or verticalacceleration. The potential for the determination of the attitude of thecarrier and its changes, which also contribute to the kinematicacceleration, are not utilized.

This way, a higher frequency (1 Hz or more) determination of signals ofthe gravity field becomes impossible from the beginning and theresolution achieved, e.g., of airborne gravimetry is limited to 10 km ormore, therefore a as such desirable greater application is hindered.

Also the hitherto necessary utilization of bigger vehicles limits theoperation in lower flight altitudes and more shallow waters,respectively, and consequently the recovery of finer structures of thegravity field.

Also, the possibility has not been utilized so far to make use of the apriori knowledge of the stochastic characteristics of the terrestrialgravity field when filtering the observations.

Therefore, the basis of the present invention is the task to give ageneric device and method, respectively, allowing a higher resolution,i.e., a recovery of finer structures of the gravitational field of theearth particularly from an aircraft or ship. Above this, the utilizationof more simple device components shall be facilitated. The determinationof all three components of the gravitational field of the earth by meansof vector gravimetry shall be made possible with adequate accuracy.

According to the invention the objects are solved by the characteristicsgiven in patent claims 1, 8 and 9.

SUMMARY OF THE INVENTION

Gravitation in three dimensions is measured using an accelerometerattached to a carrier, a satellite navigation receiver and a computer.The satellite navigation receiver determines a position and attitude,and changes in the position and attitude over time. The computercalculates complete kinematics in inertial space from the timely changesof the determined position and attitude and calculates the gravitationby subtracting the kinematic acceleration from the one observed by theaccelerometer.

In a preferred embodiment the accelerometer is connected tightly to thecarrier. At most, damping elements may be mounted between theaccelerometer and the carrier. The accelerometer can be a singleaccelerometer or a triplet of non-parallel accelerometers. The satellitenavigation receiver may be one instrument equipped with three or moreantennae or a set of three or more single instruments connected to eachother.

A time signal of the satellite navigation receiver is used forsynchronizing the acceleration measurements. More specifically, the timesignal of the satellite navigation receiver may be utilized forcontrolling the gate time of a counter, which counts an accelerationproportional frequency generated for signal evaluation.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 depicts a filter model for filtering accelerometer measurements.

FIG. 2 shows the relationship between geocentric, inertial,accelerometer and carrier reference frames.

FIG. 3 depicts the signal flow between an accelerometer and a computer(which may be repeated for each of three accelerometers) in a preferredembodiment of the present invention.

FIGS. 4A shows the vertical component of gravitation as measured duringa flight over a part of the Bavarian Alps using the present invention,and FIG. 4B shows gravitation along the same flight path computed solelyfrom topographic data.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention submitted hereby reduces the necessary expenditure ofconstruction and consequently the costs of observations and increasesthe spatial resolution and therefore the performance significantly.

The invention is based on the recognition that by means of satellitenavigation also the attitude of a carrier bearing the gravitationalsensor may be determined. The temporal change of position and attitude,directly transformable to inertial space by means of the satellitenavigation system, allows the computation of the kinematic accelerationb including the contribution of the rotation of the carrier and therebya reduction of the accelerometer signal a according to g=a-b , hence thecomputation of gravitation, as will be explained in detail below. Thecontribution to b by the rotation of the carrier is depending e.g., onthe arrangement of the accelerometers at the carrier, it is, however,usually so large that it may not be neglected. This confirms thenecessity of the determination of the attitude.

In accordance with the instrumental accuracies achieved today, b can bedetermined by satellite navigation to 10⁻⁶ of the gravitation of theearth and hence about as accurately as a and the accuracy target for gby airborne or ship borne gravimetry; these figures refer to mean valuesper second.

According to the invention the proposed persistent utilization ofsatellite navigation makes possible not only the determination of thekinematic acceleration b in one direction but as a full vector b (in thefollowing underlining as e.g., b explicitly indicates the vectorproperty).

One advantage of satellite navigation is the small phase lag betweensignal input (change of position) and signal output (quotation ofposition) and the capability for its calibration. This property isutilized more thoroughly in this case for the determination of (highfrequency) accelerations than e.g., for positioning and attitudedetermination in aerophotogrammetry. This facilitates the integration ofb with other observations in phase.

The invention renders possible the utilization of high-grade marketableaccelerometers instead of specialized gravimeters. One advantage is thelower price.

These accelerometers may be mounted in any direction, in contrast tospecialized gravimeters, therefore they may be fitted firmly to thecarrier--at most separated by damping elements. This fact saves theexpenditure for a gyro-stabilized platform. The vibrations of thecarrier--e.g., because of the engine--in general lead via the so calledrectification to a constant bias of the reading of an accelerometer.Because of the constant geometry of the source of vibrations and theaccelerometer, errors caused by changes of geometry are avoided--incontrast to when utilizing a gyro stabilized platform.

Another advantage over special gravimeters lies in the shorter naturalperiod, i.e., small phase lag between signal input (acceleration) andoutput (electrical signal) in the interesting frequency band. This factrenders possible the integration of acceleration with other observationsin correct phase.

Consequently, jointly with an accelerometer triplet firmly mounted("strap down") to the carrier providing the observed acceleration vectora, the determination of the vector of gravitation g becomes possibleaccording to g=a-b, i.e., vector gravimetry.

The integration of the two signals a and b mentioned above maintainingtheir phase relation requires a simultaneous trigger signal for callingboth values. For this purpose, the 1 pps (1 pulse per second) signal isused, available in most professional GPS receivers and controlled byatomic clocks aboard the satellites and therefore exhibiting highestprecision. This opens the possibility of an integration at a highsampling rate 1 Hertz or more) and realizing of the above formula g=a-b(scalar or vector) for each single observation. The high sampling rate,in turn, makes possible a high spatial resolution of the gravity fieldfrom a moving carrier. For example, a sampling rate of 1 Hz in a lightpropeller aircraft results in one observation per 50 m distancetraveled. This is a better basis for a high resolution as withconventional airborne gravimetry, regardless of the filtering necessaryin any case.

Another embodiment of the invention is the utilization of the precisetime of the satellite navigation system for controlling the readoutelectronics connected to the accelerometer. The accuracy of therealization of the integration interval has to be in accordance with theaccuracy desired for the signal a ; this one, however, is adapted to thedesired eventual accuracy of 10⁻⁶ (or better) of the gravitation of theearth. Consequently, using e.g., a sampling rate of 1 Hz, the gate timeof the counter used has to be controlled to 10⁻⁶ s (or better). Insteadof an otherwise also possible solution using a high-grade clock, the 1pps-time signal of the satellite navigation system mentioned above wasutilized, further reducing the total expenditure.

In the framework of the invention an advanced numerical filtering methodis applied. This method is based on the recognition that the mainproblem of gravimetry aboard moved carriers, the separation of kinematicand gravitational acceleration observations with accelerometers, may bebased on the fact that the gravitational field may be considered astochastic process (i.e., random process), certain parameters of whichare known; simply speaking, one knows from experience, by how much onthe average gravity field changes over some distance. Knowing the courseor the velocity, respectively, of the measuring vehicle, this functionof position (more precisely: of the distance) may be transduced to afunction of time. These now timely variations of the gravitationalcontribution to the signal are of low frequency compared to the motionsof the carrier (e.g., aircraft or ship). In general, therefore, alowpass filter for the observation signal a has to be designed in orderto compute the low frequency contribution g. The numerical filters usedfor this purpose so far are using arbitrary methods, for which softwareis available; the coefficients of these are fitted by experiment inorder to achieve an optimum result, i.e., the known a priori informationon the stochastic properties of the gravitational field is not utilized.In the framework of this invention the so-called dynamics matrix F_(n)of a shaping filter as part of a Kalman filter is designed by means ofappropriate programs such that the stochastic behavior of the stateparameters for the gravitation g corresponds to the stochastic behaviorof the real gravitational field. The contribution to the entireinvention consists of the development--on the basis of the well knownKalman filtering and shaping filters (c.f. P.S. MAYBECK: StochasticModels, Estimation and Control, vol. 1 & 2; Academic Press, Inc., Bostonetc. 1979 and 1982; particularly vol. 1, p. 8, 180ff, 186ff, 316, 321,345; vol. 2, p. 54)--of a method for the numerical approximation of thedynamics matrix F_(n) by the numerically given covariance of thegravitational field (H. K. NEUMAYER: Modellierung stochastischkorrelierter Signalanteile in geodatischen Beobachtungen, angewendetinsbesondere auf die Bestimmung des Schwerefeldes aus der Kombinationvon kinematischen und dynamischen Messungen; Dissertation TU Munchen,erscheint 1995, Modeling of stochastically correlated signalconstituents in geodetic observations, applied particularly to thedetermination of the gravity field by the integration of kinematic anddynamic observations; PhD dissertation, Technical University Munich, toappear 1995!). The low pass filter designed accordingly therefore isphysically based on the stochastic behavior of the gravitational fieldand hence performs better than a `physically blind` low pass filter.

The role of F_(n) in the framework of the filter model is explained bythe filter diagram depicted in FIG. 1, where the shaping filter ispresented as a subsystem of the total system in the left part and thevariables are: w_(n) =white noise driving the shaping filter, F_(n)=dynamics matrix of the shaping filter, n=output of the shaping filter,F=dynamics matrix for the other (deterministic) states, w=white noisedriving the main system, x=states, H=observation matrix, v=residuals,z=observations.

The basis of the mathematical-physical model can be explained by meansof the following formula and FIG. 2:

    r.sub.im =R.sub.i.sup.g (r.sub.gl +R.sub.g.sup.l R.sub.l.sup.b (r.sub.ba +R.sub.b.sup.a r.sub.am))

where the r's are vectors and the R's are rotation matrices,respectively.

In the above formula, the position of a proof mass m of an accelerometerin inertial space is described by the position referred to theaccelerometer itself and a sequence of transformations.

The vectors r_(ij) are explained by the sketch in FIG. 2, the R_(i) ^(j)are rotation matrices between the reference frames. The quantities withindices `am`, `ba` and `ab`, respectively, are given by instrumentalconstants and reference to the system of the GPS antennae, which can bedetermined by a conventional survey; the quantities with indices `lb`,`lg`, and `gl`, respectively, result from GPS positions--and attitudeobservations. The second derivative of r_(im) with respect to timeyields the acceleration in inertial space, denoted by b above.Subtracting the computed kinematic acceleration b from the observedacceleration a, the gravitational acceleration g sought for remains.This quantity is affected by various noise. The filtering has beenexplained above.

The concept of the solution described is particularly suited for vectorgravimetry, in the realization example one accelerometer was used forthe time being. The submission leaves the number of accelerometers usedopen, the presentations are valid for one as also for several.

An accuracy interesting for gravimetry aboard moving carriers is about 11 0⁻⁶ g₀, where g₀ is the earth's gravitation, the kinematicaccelerations are also of the order of magnitude of g₀. The design hasto be in line with these quantities and accuracy, respectively.

For the new method described herein one needs instead of an expensiveairborne/ship borne gravimeter (some 100,000.-DM) a relatively cheap(approximately 10,000.-DM) accelerometer of sufficient resolution, smartelectronics for signal processing and a special GPS receiver, thatallows to determine not only the position (relative to mm/cm accuracy)but also the attitude of the carrier (to a few 0.01°). A numericalfilter described above has to be supplemented.

With respect to the collaboration of the components and the signal flow,the configuration consists of the following components depicted in FIG.3:

Reference number 1 denotes one or several high-sensitive accelerometers.Output is an electrical current I proportional to the acceleration (in adefined direction). The raw accelerometer 1 has been mounted into around borehole of a cube of cast steel.

This one is insulated at its outer faces. The cube is mounted on a platewith levels and three foot screws, this one in turn onto a second plate,which is connected to the carrier (aircraft I ship) via dampingelements. The mounting has the following aims: The raw accelerometer asa cylinder with three flanges and a total extension of about 3 cm isoriented unambiguously by the mounting, hence it can be surveyedrelative to e.g., satellite navigation antennae with respect todirection and position. The cast steel (if possible authentic steel), byits combined characteristics of heat capacity, heat conductivity andsmall thermal expansion in connection with the insulating coating, takescare that abrupt ambient temperature changes cause only small and slowtemperature changes in the accelerometer 1 itself; these are measuredinternally and used for corrections. Active thermal control becomesobsolete by this construction. The mass of the steel cube in connectionwith mechanical damping elements cause the damping of high frequencyvibrations of the aircraft. The foot screws, in connection with bubbles,allow to put the accelerometer into the plumb-line.

The varying current I is transduced to a varying voltage U by means of acurrent-voltage transducer.

The voltage U controls a frequency F by means of a VCO (voltagecontrolled oscillator 3. The components 2, 3 are adapted to current Ifrom the accelerometer 1 as to generate a frequency of about 2 MHz at anacceleration g₀.

The GPS-receiver 4 emits every second position (3D, relative to mm),velocity and attitude of the aircraft, i.e., roll, pitch and heading ina global system. Further, one pulse per second can be utilized. Becausethe internal clock of the receiver is controlled by the atomic clocksaboard the GPS satellites, the time pulse ("1 pps") is better than1×10⁻⁶. Instead of a receiver of the GPS system also a similarlydesigned receiver in a different satellite positioning system may beused, e.g., of the GLONASS system. GPS currently is most widely used.

The counter electronics 5 has the following characteristics: Once persecond it counts approximately 10⁶ oscillations F from the VCO 3. The 1pps signal of the GPS receiver 4 guarantees that the acceleration valuesfrom the accelerometer 1 and from the GPS receiver 4 be taken strictlysimultaneous. Furthermore, the high accuracy of the 1 pps better than1×10⁻⁶ guarantees the number of oscillations be counted correctly byprecisely realizing the counter gate time. The counter electronics 5also serves for the 1 pps-pulse conditioning. Two single counters in theelectronics count alternating and without any dead time. In thecurrently non-busy counter the digital value of 21 bit word length ispassed to a recording PC 6.

EXAMPLE

The configuration as mentioned in the text above, has been realized withthe following instruments/components:

Accelerometer 1 of Sundstrand company, QA 3000-20

Current-Voltage transducer 2 by standard component with low drift andlow temperature effect

Voltage controlled oscillator 3 as standard component with low drift andlow temperature sensitivity

GPS-receiver 4: Ashtech3DF of Ashtech company

Counter electronics 5

PC 6: notebook

In connection with the embodiment the utilization of the GPS system wasanticipated. Likewise, a different suitable satellite navigation systemcould be utilized, currently e.g., GLONASS.

FIG. 4 depicts the graphical representation of preliminary results of atest flight over a part of the Bavarian Alps using the above equipmentin a one-engine propeller aircraft of the type Cessna 206. The GPSantennae were mounted to the top side of the aircraft, the very smalland compact instrumental equipment was in the interior of the aircraft,where the accelerometer was connected firmly to the aircraft via theseat rails. The digital mean accelerometer readings every second werestored in a notebook computer, the GPS observations taken simultaneouslywere stored in the receiver itself. The synchronization utilized the 1pps signal. As is usual process in geodetic GPS observations, areference receiver at the airport was used, because only differentialobservations guarantee a sufficient accuracy. The data were processedafterwards, i.e., the formula given above was evaluated, the secondderivative with time taken for the inertial accelerations, thesesubtracted from the measurements of the accelerometer and the resultfiltered consistent with the filter model presented above. The resultfor the vertical component of gravitation is depicted in the FIG. 4A;the referring profile was about 38 km in length, a profile shifted byabout 5 km was taken for the return flight. One recognizes thestabilization phase of the numerical filter at the beginning (upperleft) and after the turn (right), respectively. In FIG. 4B one can seethe values of gravitation along the flight path computed fromtopographic data. The vertical extension of a partial diagram isequivalent to about 80 mGal=80 10⁻⁵ ms⁻². Because the topographyexplains only a part of the variations of gravitational field, aconclusive error estimation is not possible using this way only, anaccuracy of 10 mGal has been achieved already along with a highresolution; it seems that an accuracy of 1 mGal along with a spatialresolution of 1 to 3 km by airborne measurements very likely can beachieved. Maintaining the concept, further improvements of detailsshould allow an accuracy improvement to 0.5 to 0.1 mGal.

We claim:
 1. A device for the measurement of gravitation, comprising:anaccelerometer attached to a carrier for observing acceleration of thecarrier, a satellite navigation receiver attached to the carrier, and acomputer coupled to the satellite navigation receiver and theaccelerometer, characterized in that the satellite navigation receiverdetermines a position and attitude, and the computer calculates completethree-dimensional kinematics, including three-dimensional kinematicacceleration, in inertial space from timely changes of the determinedposition and attitude and calculates the gravitation by subtracting thekinematic acceleration from the acceleration of the carrier observed bythe accelerometer.
 2. The device of claim 1, characterized in that theaccelerometer is connected tightly to the carrier, where at most dampingelements may be mounted between the accelerometer and the carrier. 3.The device of claim 1, characterized in that the accelerometer isselected from the set consisting of a single accelerometer and a tripletof non-parallel accelerometers.
 4. A device for the measurement ofgravitation, comprising:an accelerometer attached to a carrier forobserving acceleration of the carrier; a satellite navigation receiverattached to the carrier; and a computer coupled to the satellitenavigation receiver and the accelerometer; wherein the satellitenavigation receiver determines a position and attitude, and the computercalculates complete three-dimensional kinematics, includingthree-dimensional kinematic acceleration, in inertial space from timelychanges of the determined position and attitude and calculates thegravitation by subtracting the kinematic acceleration from theacceleration of the carrier observed by the accelerometer; and thesatellite navigation receiver is selected from the set consisting of oneinstrument equipped with three or more antennae and a device of three ormore single instruments connected to each other, which allow thedetermination of the attitude angles.
 5. A method measuringthree-dimensional gravitation using an accelerometer and a satellitenavigation receiver attached to a carrier, comprising the stepsof:measuring acceleration of the carrier with the accelerometer;utilizing the satellite navigation receiver to determine athree-dimensional position and attitude and changes thereof over time;and determining, from the changes in three-dimensional position andattitude over time, complete three-dimensional kinematics, includingthree-dimensional kinematic acceleration, of the carrier in inertialspace, and combining the measured acceleration of the carrier with thedetermined three-dimensional kinematic acceleration in order to generatethe three-dimensional gravitation.
 6. The method of claim 5,characterized in that a time signal of the satellite navigation receiveris utilized for the observation of acceleration.
 7. The method of claim6, characterized in that the time signal of the satellite navigationreceiver is used for the synchronization of the accelerationmeasurement.
 8. A method measuring three-dimensional gravitation usingan accelerometer and a satellite navigation receiver attached to acarrier, comprising the steps of:measuring acceleration of the carrierwith the accelerometer; utilizing the satellite navigation receiver todetermine a three-dimensional position and attitude and changes thereofover time; and determining, from the changes in three-dimensionalposition and attitude over time, complete three-dimensional kinematics,including three-dimensional kinematic acceleration, of the carrier ininertial space, and combining the measured acceleration of the carrierwith the determined three-dimensional kinematic acceleration in order togenerate the three-dimensional gravitation; characterized in that thetime signal of the satellite navigation receiver is utilized forcontrolling a gate time of a counter, which counts an accelerationproportional frequency generated for signal evaluation.
 9. The method ofclaim 8, characterized in that the signal transduced to an accelerationproportional frequency is evaluated in a constant sampling ratealternately by two counters such that no dead time occurs.
 10. A methodmeasuring three-dimensional gravitation using an accelerometer and asatellite navigation receiver attached to a carrier, comprising thesteps of:measuring acceleration of the carrier with the accelerometer;utilizing the satellite navigation receiver to determine athree-dimensional position and attitude and changes thereof over time;and determining, from the changes in three-dimensional position andattitude over time, complete three-dimensional kinematics, includingthree-dimensional kinematic acceleration, of the carrier in inertialspace, and combining the measured acceleration of the carrier with thedetermined three-dimensional kinematic acceleration in order to generatethe three-dimensional gravitation; characterized in that theacceleration values output by the accelerometer and the determinedposition and attitude from the satellite navigation receiver are inputto an integrating digital filter.
 11. The method of claim 10,characterized in that the digital filtering is performed using a shapingfilter fit to stochastic behavior of a gravity field.
 12. The method ofclaim 7, characterized in that the time signal of the satellitenavigation receiver is utilized for controlling a gate time of acounter, which counts an acceleration proportional frequency generatedfor signal evaluation.
 13. The method of claim 5, including tightlycoupling the accelerometer to the carrier, where at most dampingelements may be mounted between the accelerometer and the carrier.